Magnetic Resonance Imaging (MRI) techniques can be utilized for the clinical evaluation of various diseases. Some of these techniques use compressed sensing. One such compressed sensing MRI technique performs accelerated Diffusion Spectrum Imaging (DSI). In DSI, the information is encoded in both q-space (Cartesian sampling) or diffusion space and image space. The q-space information may then be used to characterize the diffusion properties of water molecules.
By applying a series of diffusion encoding gradient pulses in multiple directions and strengths, a three-dimensional characterization of the water diffusion process may be generated at each spatial location (image voxel). The MR signal in q-space is generally related to the water displacement probability density function at a fixed echo time by the Fourier transform. The diffusion information encoded in q-space may be separated into both angular and radial components. The angular component reflects the underlying tissue anisotropy, whereas the radial component provides information about the eventual geometric restrictions in the diffusion process.
Conventional DSI techniques provide acceptable information for the diffusion properties of water in the brain or other organs. However, the high dimensionality of DSI (i.e., three dimensional in both spatial and in q-space domains) requires the patient to be scanned for an extended period of time, which substantially limits the effectiveness of the conventional DSI technique when utilized in vivo.